The mean lifetime of a system is 620 hours. There are two failure types: Repairing the system after a type 1-failure requires 20 hours on average and after a type 2-failure 40 hours on average. 20% of...

The mean lifetime of a system is 620 hours. There are two failure types: Repairing the system after a type 1-failure requires 20 hours on average and after a type 2-failure 40 hours on average. 20% of all failures are type 2-failures. There is no dependence between the system lifetime and the subsequent failure type. Upon each repair the system is 'as good as new'. The repaired system immediately resumes its work. This process is continued indefinitely. All life and repair times are independent.

(1) Describe the situation by a semi-Markov chain with 3 states and draw the transition graph of the underlying discrete-time Markov chain.

(2) Determine the stationary state probabilities of the system.